Nonuniversality of Tricritical Behavior

Abstract

Deviations from the classical phenomenological theory of tricriticality are analyzed on the basis of the exact solution (in four field variables) of the spherical-model limit ($n\to \infty$) in three dimensions. The scaling functions are nonuniversal but are parametrized by a single variable, which vanishes for infinite-range interactions. Special relations between critical amplitude ratios correlate well with observations on antiferromagnets and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures. Novel qualitative predictions are made for the threephase monohedron below $T_t$.